"People, the lawyers and the courts can call it whatever they want, but I am calling it what we need and what it is, a TRAVEL BAN!" Trump tweeted.

He said in another tweet that the Department of Justice should have stuck with the original travel ban as opposed to the second version of the executive order, which rolled back some of the more controversial aspects of the first executive order.

Gorka took to the airwaves soon after and defended Trump's tweets when Cuomo suggested they had erased the administration's efforts to move away from calling the executive order a "travel ban."

"You guys played games about it and said it's not a ban," Cuomo said. "I could play you Sean Spicer right now, and you know it's true. Then, the president decides to be honest about it this morning."

Cuomo continued: "This is spin. You are the purveyor of spin, because that was your message — that it wasn't a ban. And it was untrue."

Gorka said the Obama administration was also a "purveyor of spin with that calculation." He explained that Trump's executive order was based on the Obama White House's analysis of the seven nations that pose the biggest threat to the US with respect to immigration.

Cuomo said the Obama administration's policy was aimed at targeting travel to those countries.

"Your order is about Muslims. About targeting Muslims and keeping them out and allowing those who are not Muslim a carve-out to come in," he added.

Cuomo was referring to the original travel ban, which banned most refugees from those countries but made an exception for some Christian refugees. That stipulation was dropped in the second executive order after Trump faced backlash for what critics said was religious discrimination.

Gorka said that Indonesia and Egypt were respectively the largest Muslim and Arab nations, and that if Trump's executive order were targeting Muslims, travelers from those countries would have been included.

Why would they "not be included in the executive order? Explain that logic to me, because this is where your spin fails, this is where the fake news propaganda collapses," Gorka told Cuomo.

"If we had some dark ... motive, those are the two first nations you would put on the list, not the seven nations the Obama White House identified" as the greatest concern, "so please answer that question," Gorka continued.

Cuomo said that instead of focusing on who wasn't included in the travel ban, it was important, "for legal and policy purposes," to examine who was included. "And those countries are all Muslim-majority, you did a carve-out for non-Muslims, and that's why it got struck down originally," Cuomo said.

Cuomo later said that Trump confirmed the executive order was a ban, and that "he likes that it's a ban, he likes the original ban, and that's what he wants everybody to know. Why play the games?"

"There are no games. The president can call it whatever he likes," Gorka said, because Trump "has the constitutional authority" to make policies regarding immigration and national security.

"If he wants to call it a ban, he's the president, he's the chief officer of this administration, and he has every right to do that," Gorka said.

White House counselor Kellyanne Conway also suggested Monday that the media covers too much of Trump's tweets.

"But, you know, this obsession with covering everything he says on Twitter and very little of what he does as president —" Conway said on the "TODAY Show."

"Well, but that's his preferred method of communication with the American people," host Craig Melvin said in response.

"That's not true," Conway said.

"Well, he hasn't given an interview in over three weeks. So lately, it has been his preferred method," Melvin said.